Help with Convection/Cooling System

I am looking to send compressed air into a temperature chamber which will be cooler than ambient . The air is to be utilized inside the chamber but before it is I want to make sure it has dropped to the temperature of the chamber so pressure readings wont be skewed.

I am envisioning some sort of copper tube system that the air will flow through in the chamber (already cooled) before it is used, I need help figuring out the length and size of tube that would be required to ensure my temp drop is reached.

I was thinking it would be along the line of Q=hA(Tw-Tt) This wont help me figure out the tubing required though because I don't know Q ahead of time or do I?